Near the end of The Artist, George Valentin is looking at his own reflection superimposed on a tuxedo in a shop window (the scene used in the trailer) when a cop comes strolling around the corner. George notices him and his smile fades. The cop approaches George with a seemingly friendly manner and speaks to him but there's no title card so we (at least those of us who don't lip-read!) can't tell what he is saying. The camera dwells on him for some time, cutting to a very tight close-up on his mouth as he talks, and then we see George backing away, looking confused or possibly disturbed.

6 Answers
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Mark has a good interpretation. But I feel it's a bit simpler than that: this is the point at which George realizes what the rest of the public has already determined - that when you see a mouth move, something should come out. By seeing the cop's mouth move, but not being able to hear anything, George sees that he was wrong about talkies not being the future.

There's only one explanation I can think of, which involves some spoilers:

In the final scene we discover that George has a thick French accent. This helps explain his reticence to move into talky films, which up until this point we thought was only down to pride. Perhaps all along George believed that audiences would want their talky stars to have all-American accents, hence his clinging on to the silent era. (This theory is also supported by the fact that neither Peppy nor the studio boss argues with George's assertion that nobody would want to hear him talk.)

So I wonder if what's happening in this scene is that George doesn't really hear what the cop is saying (hence the lack of title card), all he hears is his American accent: the one thing George can never have, and which he believes has cost him everything. After this scene he goes back to his burnt-out apartment, sits at his bureau, and faces start appearing round him: again, they're talking but we get no title cards, and again it ends up zooming on just on the mouths.

What the people are saying isn't important: it's the fact that they're talking (or how they're talking) that's significant. George has become completely preoccupied with his accent, tormented by how effortlessly other people do what he can never do (speak with an American accent), and it is this that drives him to contemplate suicide.

I think the answers are complicating the scene. I have actually worked on the publicity of the film in East Asia and discussed the film in depth with experts for rating purposes, so here's what I know from there.
In this scene, George Valentin realizes that the world around him has audible speech. Now, when he hears the cop speaking, it hits him hard that everyone does actually have sound and it will soon hit the movies. Thus, hurting his ego even further that he was wrong flaunting his pride.
The scene where we cut to a lot of mouths speaking create a disturbing and disorienting noise for him driving him to attempt suicide.
There is so much noise in the world, that its amplified in his head, there is no place for a proud silent star.

The scene featuring the policeman talking at George parallels the opening clip of the character in the movie-within-the-movie being tortured by sound. Perhaps the simple answer to the policeman-scene's importance is that sound, or too much talk, does assault the ears.

Yet his wife, portrayed as pretty bland and humorless, needs words, needs George to prattle. Maybe, then, the movie is suggesting that instead of talking, a bit of "mugging," as Peppy would phrase it, is charming, a good thing, especially if the alternative is inane drivel. Charm does seem to rely on the unspoken, the subtle; the overt tends to rob the imagination... And as for George's single utterance? It has a certain je ne sais quoi, n'est-ce pas?

I would offer this: What nationality were cops portrayed as back then? The answer: IRISH. I would bet that both the cop and all the other "mouths talking" had accents, thus amplifying George's own predicament.

Artist in the first layer, gives a very strong story about a period of time in film history that some main actors of silent era fall from their popularity, the other good example of this kind of caters is Sunset Blvd.

In this scene Valentin sees himself in the reflection of the mens furnishing shop, first to remember about the elements of attraction in science, second to remind us about most important reason to be an actor on that time, the body.

If we remember the first dancing scene behind the curtain by Valentin and Peppy Miller remember that the director shows us only the foot of Miller because the important element is the body.

By interring the police as a representation of the society norm, Valentine came back from his imagination, the reflection, to the real world, and importance of speaking in life more than body.

As we see the police officer is very still and we see from his long shot to his mouth closing up, this new norm embarrassing him. The director emphasized on this change by the previous scene when Valentin sees all of his staff in the store and not any more in the guest room or other places.